By Ron Larson
CALCULUS I WITH PRECALCULUS, brings you in control algebraically inside of precalculus and transition into calculus. The Larson Calculus application has been largely praised by means of a new release of scholars and professors for its good and powerful pedagogy that addresses the wishes of a wide variety of educating and studying types and environments. each one name is only one part in a finished calculus direction software that conscientiously integrates and coordinates print, media, and expertise items for profitable instructing and studying. One basic target guided the authors in scripting this booklet: to increase unique, readable fabrics for college kids that in actual fact outline and show thoughts and ideas of calculus.
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Additional info for Calculus I with Precalculus, A One-Year Course, 3rd Edition
All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s). Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it. qxp 14 10/21/10 Chapter P 2:16 PM Page 14 Prerequisites 150. From the foot bones of an adult human male, an anthropologist estimates that the person’s height was 69 inches.
X Ϫ 10 ϭ x 2 Ϫ 10x 93. 5 ϭ 0 94. 193 ϭ 0 95. 422x 2 Ϫ 506x Ϫ 347 ϭ 0 96. 651 ϭ 0 In Exercises 97–104, solve the equation using any convenient method. 98. 11x 2 ϩ 33x ϭ 0 x 2 Ϫ 2x Ϫ 1 ϭ 0 2 100. x2 Ϫ 14x ϩ 49 ϭ 0 ͑x ϩ 3͒ ϭ 81 102. 3x ϩ 4 ϭ 2x2 Ϫ 7 x2 Ϫ x Ϫ 11 4 ϭ 0 4x 2 ϩ 2x ϩ 4 ϭ 2x ϩ 8 a 2x 2 Ϫ b 2 ϭ 0, a and b are real numbers, a 0 In Exercises 105–118, find all real solutions of the equation. Check your solutions in the original equation. 106. 2x4 Ϫ 50x2 ϭ 0 4 108. x Ϫ 81 ϭ 0 110. x 3 ϩ 216 ϭ 0 3 2 x Ϫ 3x Ϫ x ϩ 3 ϭ 0 x3 ϩ 2x2 ϩ 3x ϩ 6 ϭ 0 x4 ϩ x ϭ x3 ϩ 1 x4 Ϫ 2x3 ϭ 16 ϩ 8x Ϫ 4x3 116.
Factor. Set 1st factor equal to 0. Set 2nd factor equal to 0. Second Equation Ϫ ͑x 2 Ϫ 3x͒ ϭ Ϫ4x ϩ 6 x 2 Ϫ 7x ϩ 6 ϭ 0 ͑x Ϫ 1͒͑x Ϫ 6͒ ϭ 0 xϪ1ϭ0 xϪ6ϭ0 Use negative expression. Write in general form. Factor. xϭ1 xϭ6 Set 1st factor equal to 0. Set 2nd factor equal to 0. Check ? Խ͑Ϫ3͒2 Ϫ 3͑Ϫ3͒Խ ϭ Ϫ4͑Ϫ3͒ ϩ 6 18 ϭ 18 ? ͑2͒2 Ϫ 3͑2͒ ϭ Ϫ4͑2͒ ϩ 6 Խ Խ Ϫ2 2 ? Խ͑1͒2 Ϫ 3͑1͒Խ ϭ Ϫ4͑1͒ ϩ 6 2ϭ2 ? ͑6͒2 Ϫ 3͑6͒ ϭ Ϫ4͑6͒ ϩ 6 Խ Խ 18 Ϫ18 The solutions are x ϭ Ϫ3 and x ϭ 1. Substitute Ϫ3 for x. Ϫ3 checks. ✓ Substitute 2 for x.
Calculus I with Precalculus, A One-Year Course, 3rd Edition by Ron Larson